Seismic imaging is used for various purposes, such as for searching for subsurface oil and gas reservoirs. In seismic imaging, a physical subsurface image or a related subsurface information model, such as the velocity model, is constructed from collected seismic measurement data. One type of collected seismic measurement data is prestack reflection data in the time domain. Generally, to collect prestack reflection data, acoustic or elastic waves are sent into the underground using a number of specialized sources. The sources are typically dispersed over the top surface to cover a certain area of interest. The reflected seismic waves from the subsurface are then collected at the top surface using a number of specialized receivers that cover the area of interest. The subsurface image, or the related velocity model, is then constructed by processing the prestack reflection data in some form.
Recently, with the rapid development of computing hardware, mathematical waveform inversion of prestack reflection data has reemerged as one form of processing to generate subsurface information from an initial guess model. Waveform inversion of prestack reflection data has been attempted in both the time domain and the frequency domain, arriving to no conclusions on which approach is best. Both approaches have been applied with degrees of success to synthetic data generated by known theoretical benchmark models. However, a successful implementation of waveform inversion for real collected prestack reflection data remains elusive. One obstacle for a successful implementation is the absence of low frequency components in real data, which makes it difficult to resolve long wavelength velocity models. Another reason that prevents a successful waveform inversion of real data is the possibility of non-unique solutions for subsurface images or velocity models.